Ind. Eng. Chem. Res. 1997, 36, 2421-2426
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Improvement of Heat Transfer in a Packed-Bed Reactor for a Chemical Heat Pump Using Sodium Carbonate Decahydrate Dehydration Yukihiko Matsumura* and Kunio Yoshida Department of Chemical System Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan
To improve the heat transfer characteristics of a gas-solid packed-bed reactor, an inert solvent was added to the reactor. For sodium carbonate decahydrate dehydration, used in a chemical heat pump, n-pentanol was chosen as a solvent, and the dehydration rate in the solvent was measured. The dehydration rate was found to be proportional to the total surface area of the decahydrate particles, and the rate equation was determined. Particle size distribution (less than 400 µm) remained unchanged for a three-time cyclic operation. The packed-bed of decahydrate with n-pentanol solvent showed considerable improvement in heat transfer characteristics compared with the case having no solvent, and cold heat generation was more than doubled. A simulation study showed that the addition of n-pentanol may make it possible to construct a high-performance heat pump with cold storage capability, attaining 280 K in less than 5 s and total heat release within 1600 s. Introduction Efficient heat transfer characteristics in a gas-solid reactor are essential for attainment of a high reaction yield and effective use of thermal energy. This requirement is especially critical when gas-solid reactions are employed in a chemical heat pump system, since the system efficiency depends on the effectiveness of heat utilization. However, for many chemical heat pump systems, packed-bed reactors have been commonly used in spite of the low effective thermal conductivity of the packed-bed particles. The temperature distribution appearing in the reactor reduces the reaction rate and demands more chemical work. Many attempts, therefore, have been made to improve the heat transfer characteristics of gas-solid reaction systems used in chemical heat pump systems. Yamazeki et al. (1991) and Murata et al. (1993) used a heat exchanger with catalyzed walls as a hydrogenation reactor for a benzene/cyclohexane chemical heat pump. For a silica gel-water adsorption chemical heat pump, Watanabe et al. (1993) employed silica gel supported on copper tubing inside which heat-removing fluid was delivered. For a chemical heat pump using the hydration of calcium oxide, Ogura et al. (1991, 1992, 1993) proposed metal fins inserted into the reactor to enhance heat transfer. Hirata and Fujioka (1993) calculated the effect of inserted stainless fins on the heat transfer characteristics of methylamination of calcium chloride in their chemical heat pump. We proposed a chemical heat pump using dehydration of sodium carbonate decahydrate with the purpose of load leveling and indicated the importance of highefficiency heat transfer in the hydration reactor (Matsumura and Yoshida, 1993, 1995). The principle of this system is shown in Figure 1. The system is composed of two vessels filled with sodium carbonate decahydrate and anhydrous oxalic acid, respectively. In the daytime, when cold heat needs to be generated, the transfer of water vapor is allowed between these vessels. The lower vapor pressure of oxalic acid drives dehydration of the decahydrate, generating cold by the dehydration †
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Figure 1. Principle of the proposed chemical heat pump system.
reaction. Oxalic acid turns into dihydrate and sodium carbonate into monohydrate after this operation. At night, a compressor is operated, consuming electricity, to generate a reverse flow of water vapor, thus returning the system to its original state. Experiments using packed-bed reactors showed lower temperatures inside the bed than those at the heat-exchanger wall, indicating the necessity of enhancing the heat transfer rate. In this study, therefore, the addition of an inert solvent is considered. The solvent fills only the space between reactant particles and does not bring about a change of reactor volume. Wentworth et al. (1981) added nheptanol to the system of calcium chloride and ammonia and measured the ammoniation rate of the chloride. They found improvement of the reaction rate, and attributed it to a higher concentration of ammonia in the solvent than that in the gas phase. This paper discusses the requirement of the solvent and proposes the addition of n-pentanol to the dehydration of sodium carbonate decahydrate. © 1997 American Chemical Society
2422 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 Table 1. Requirements for a Solvent Added to a Packed-Bed Gas-Solid Reactor for Heat Transfer Improvement 1 2 3 4 5
Proper solubility of gas reactant at the operational partial pressure of the reactant. No solubility allows no reaction. High solubility brings about volume change in the liquid phase and dissolution of the solid reactant into the solution. No interaction between the solvent and the solid reactant such a dissolution and side reaction. Low vapor pressure so as not to prevent smooth flow of gas reactant. Low cost. Low toxicity.
Figure 2. Liquid-vapor equilibrium of an ideal solution of water and solvent.
Figure 3. Liquid-vapor equilibrium of a water-n-pentanol system.
Requirements for the Solvent The solvent should not retard the main reaction rate. When finding a suitable solvent, therefore, the solubility of the gaseous reactant in the solvent is the first point to be considered since the concentration of reactant in the solvent should directly affect the reaction rate. Solvents with low solubilities for the reactant gas inhibit contact between the gas and solid reactants. For example, in the sodium carbonate decahydrate reactor, water vapor solubility in the inert solvent influences the hydration/dehydration rate. In solvents which are immiscible with water, such as silicone oil, the desired reaction cannot take place. The solubility of water at equilibrium with water vapor pressure in the process of dehydration/hydration of decahydrate is determined by calculation of the gas-liquid equilibrium. Assuming an ideal solution of water and solvent, this equilibrium is shown in Figure 2. The mol fraction of water in the liquid phase at dehydration and hydration is determined by finding the fraction which gives the vapor pressure needed for dehydration and hydration, i.e., the vapor pressure of oxalic acid dihydrate and that of sodium carbonate decahydrate, respectively. At the ideal state, these values are 0.35 and 0.63, respectively. The difference between 0.35 and 0.63 in mol fraction, namely, 0.28, is problematic: 1. The increase in liquid volume at the hydration stage requires a bigger reactor volume. 2. The high water content in the liquid phase brings about dissolution of sodium carbonate decahydrate. Consequently, it is found that high solubility of the gas reactant is not always desirable. For a gas reactant such as hydrogen, which dissolves sparingly in the liquid, this is not usually the case, but for a gas reactant with large solubility, the solution should be nonideal because the difference in operating vapor pressures does not change the mol fraction of water in the liquid phase. The second requirement for the solvent is that there must be no interaction between the solvent and solid reactant. Namely, the solvent should not dissolve the reactant to any large extent, nor should the solvent react with the solid. Heat pump systems operate cyclically, so undesirable interaction between the solvent and solid reactant causes the accumulation of byproducts during the process of cyclic operation and adversely affects the efficiency of the system.
Figure 4. Experimental apparatus for dehydration rate measurement.
Other conditions to be considered are a low solvent vapor pressure so as not to prevent smooth flow of water vapor between the vessels and, of course, low cost and low toxicity. These requirements are listed in Table 1, for reference purposes. From consideration of the above, n-pentanol was selected in this study. Figure 3 shows the gas-liquid equilibrium for the water-n-pentanol system. This system consists of two liquid phases with a gas phase when the water mol fraction is higher than 0.35, but at the vapor pressures concerned, water mol fractions in the liquid phase are less than 0.2 and water is completely dissolved to form a single liquid phase. Experimental Section Dehydration Rate of Sodium Carbonate Decahydrate in n-Pentanol. The dehydration rate of sodium carbonate decahydrate was measured in a laboratory scale reactor composed of a 500-mL conical flask with sampling equipment, as shown in Figure 4. Five grams of sieved sodium carbonate decahydrate particles (Kanto Kagaku Co.) were added to n-pentanol (Kanto Kagaku Co.) and stirred with a magnetic stirrer. The reactor temperature was controlled by a constant temperature bath. The liquid phase in the reactor was sampled through a filter by opening the sampling valve while pressurizing the system with nitrogen. The water concentration in the sample was determined by using
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2423
Figure 7. Dehydration plot for particles of different diameters. Figure 5. Packed-bed reactor.
Figure 8. Influence of particle size on dehydration rate. Figure 6. Effect of rotating speed of a magnetic stirrer on dehydration rate.
a Kirl-Fischer hygrometer (Mitsubishi Kasei, CA-06). By multiplying the obtained water concentration by the liquid phase volume, the total amount of water in the liquid phase was determined, and by dividing the amount with the initial water molecules to be removed in the decahydrate, dehydration conversion was calculated. Packed-Bed Reactor. Figure 5 shows the packedbed brass reactor (46-mm i.d., 40-mm depth) where sodium carbonate decahydrate particles were packed on a gauze. A magnetic stirrer stirred the liquid phase in the reactor under the gauze. Pure n-pentanol was added to the bed, so that whole bed stayed in the liquid phase. After a constant temperature was achieved by use of water bath, the vapor pressure over the bed was reduced to 350 Pa by a vacuum pump and a pressure control valve, to begin dehydration. Water vapor generated by dehydration was collected by the calcium chloride and, from the weight increase of the chloride, the dehydration conversion was determined. The reactor internal temperature was measured by four type-K thermocouples at different radial positions. Results and Discussion Dehydration Rate of Sodium Carbonate Decahydrate in n-Pentanol. Figure 6 shows the effect of the rotating speed of the magnetic stirrer on the dehydration rate. It is important to clarify that the mass transfer step is not affecting the dehydration rate and that the measurement is for the kinetics of the reaction itself. Since mass transfer coefficient around a particle in a flow is affected by the flow rate around the particle, a good test to see if mass transfer is affecting the total dehydration rate or not is changing the stirring speed and seeing if any influence of the speed on the dehydration rate exists. No influence should be found when the mass transfer step is not significant. Good reproducibility under different rotating speeds shown in Figure
6 indicates that the mass transfer step outside the particle is not rate-determining and assures that the measured dehydration rate here is for the reaction itself. Figure 7 shows the change in hydration conversion with time at 298 K. As dehydration goes on, the monohydrate produced is removed from the surface of the original particles and the reduction in particle size is observed. The reason for the retardation of hydration rate observed at high conversion is that the surface area of the decahydrate particles decreases and that water concentration in the liquid phase increases. A higher dehydration rate for smaller decahydrate particles also indicates that dehydration rate is largely affected by surface area. To eliminate the effect of increasing water concentration in the solvent during the dehydration, the initial rates of dehydration are adopted for the analysis. The relationship between the particle size and dehydration rate is shown in Figure 8. Since the number of the particles and the surface area of a single particle are proportional to the minus third and the second power of the particle size for a specific molar amount of reactant particles, respectively, total surface area, obtained as a product of these two values, is in proportion to the minus first power of the particle size. Thus, when the reaction is proportional to the total surface area of the particles, namely, the surface reaction is rate-determining, the slope of the plot showing the relation between particle size and reaction rate should give a value of -1. Figure 8 shows that it is the case for this system and, thus, that the dehydration rate should be evaluated on a unit surface area basis. The effect of initial water concentration ranging from 32 to 1390 mol m-3 is shown in Figure 9. A high water concentration reduces the rate of dehydration. This fact implies that the reverse reaction, hydration of the product monohydrate, is also taking place, as well as slowing down the overall dehydration rate. It is known that when the chemical potential of the reactant and product are the same, the overall reaction rate becomes
2424 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
Figure 9. Influence of initial water concentration on dehydration rate.
Figure 11. XRD diagrams of rehydrated particles, sodium carbonate decahydrate, and sodium carbonate monohydrate.
Figure 10. Relationship between ∆CW ) CSC - Cw and dehydration rate.
zero. Thus, at the water concentration represented by CSC, which is at equilibrium with the water vapor pressure of the decahydrate at the operating temperature, the reaction rate should be zero, and the difference between CSC and the concentration for the operation condition represented by Cw can be taken as the driving force of the dehydration. Figure 10 shows the relationship between this concentration difference and the reaction rate. Surprisingly, it shows no dependence on temperature under the present experimental conditions. The hydration rate is expressed as
rs ) k(CSC - Cw)n k ) 1.16 × 10-12 mol1-n s-1 m3n-2 n ) 2.68
(1)
The independence of temperature observed here implies that a certain mass transfer step may be ratedetermining. When a simple mass transfer step is the rate-determining step, however, the index of the concentration driving force, CSC - Cw should be unity. A more complex mechanism must be considered to explain the dehydration observed here. For example, we found the hydration rate of magnesium oxide in triethylene glycol was proportional to the amount of adsorbed water molecules (Matsumura et al., 1995). The reaction mechanism should be elucidated by a further study. Cyclic Reaction. A cyclic operation of dehydration/ rehydration is essential to a chemical heat pump. After dehydration of decahydrate particles in n-pentanol, the particles were collected and rehydrated in a n-pentanol solution with a water concentration higher than the equilibrium value. XRD diagrams for the product shown in Figure 11 indicate that decahydrate is reproduced by such a rehydration treatment. No side product is observed, which is significant for the chemical heat pump operation. The particle size distribution was measured by a laser diffraction particle size analyzer
Figure 12. Change of particle size distribution in cyclic operation.
(Shimadzu, SALD-1100) after the first, second, and third dehydration/rehydration cyclic operations. Figure 12 shows the particle size change during these operations. After first dehydration, particle size reduced to less than 400 µm. Considering the fact that the initial particle size is between 840 and 1000 µm, the particle size distribution remains constant throughout this cyclic operation after the first dehydration. The cyclic operation of dehydration/hydration is carried out smoothly, showing no problem caused by change in physical and chemical characteristics through cyclic operation at least for three cycles. Packed-Bed Reactor. Temperature changes inside the reactor with time during dehydration at four radial positions are shown in Figure 13. A flat temperature profile in the radial direction indicates the heat transfer rate through the bed was fast enough to avoid hindrance caused by slow heat transfer. This result is remarkable considering the fact that in a packed-bed reactor sometimes a temperature difference greater than 4 K is observed (Matsumura and Yoshida, 1995). This large temperature difference means a low temperature inside the bed, decreasing the dehydration rate to a very small value. The power as a cold heat generator is reduced severely. The conversion change with time is compared with that of the nonsolvent system in Figure 14, from which it can be seen that a much faster dehydration rate compared to that of the nonsolvent system is achieved for solvent added system. After 5 h, the
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Figure 13. Temperature changes during dehydration in a packedbed reactor with n-pentanol.
Figure 16. Conversion change simulated for dehydration of sodium carbonate decahydrate in a chemical heat pump.
Figure 14. Comparison of conversion change with time between solvent and nonsolvent cases.
up ability of this chemical heat pump. Quick response of a heat pump system is an important feature considering the commercialization of the system. Attainment of 280 K in less than 5 s indicates that only the refrigerant delivery time is needed to start up the air conditioning system using this heat storage device. The conversion change with time shown in Figure 16 indicates that dehydration can be completed in 1600 s. Since the peak load requirement is for 2 or 3 h in the hottest period, all the stored heat can be released when it is needed. This quick reaction rate also indicates high cooling power of this system, since it allows a sufficient reaction rate even at a temperature less than 280 K, thus lowering the refrigerant temperature. Conclusions
Figure 15. Simulated temperature change in a sodium carbonate decahydrate reactor.
conversion for the solvent added system is twice as big as that for the nonsolvent system. This indicates a doubling of the cold heat generation power. Decrease in particle size results in more improvement, which is possible only for the solvent added system, for utilization of fine powder reactant in the nonsolvent system results in formation of a reactant agglomerate of low reactivity. Calculated Performance of the Chemical Heat Pump. Based on the dehydration rate obtained in this study (eq 1) and the particle size distribution (Figure 12), changes in the temperature and conversion of sodium carbonate decahydrate in the chemical heat pump were calculated. The system is at 300 K at the beginning, and dehydration is started by decreasing the water vapor pressure to 349 Pa. The heat transfer step is assumed to be much faster than the dehydration rate. As the dehydration takes place, the temperature of the system decreases due to the endothermic reaction. Once the temperature reaches 280 K, the temperature of the vessel is kept at that temperature by recovering cold heat for air-conditioning purposes. The solid volume fraction is 0.4. Figure 15 shows the temperature change in the reactor: in less than 5 s, the temperature in the reactor reaches 280 K and demonstrates the quick start-
(1) The requirements for the solvent added to packedbed reactors were discussed. Proper solubility of the gas reactant, no undesirable interaction between the solvent and the solid reactant, low vapor pressure, low cost, and low toxicity should be required of the solvent. (2) To improve heat transfer characteristics of a packed-bed reactor of sodium carbonate decahydrate, n-pentanol was selected. (3) The dehydration rate of sodium carbonate decahydrate was measured in n-pentanol solution, and a rate in proportion to the surface area of decahydrate particles was observed. A rate equation for a unit surface area of particles was determined. (4) Cyclic operation of dehydration/rehydration could be carried out with a stable particle size distribution (less than 400 µm). (5) A packed-bed reactor with n-pentanol between sodium carbonate decahydrate particles showed a sufficiently high heat transfer rate through the bed, doubling the cold heat generation rate compared to that of the nonsolvent system. (6) Simulation based on the dehydration characteristics indicated attainment of 280 K in less than 5 s and release of stored cold heat within 1600 s, showing the possibility of a high-performance air conditioning system. Nomenclature CSC ) water concentration at equilibrium with vapor pressure of sodium carbonate decahydrate, mol m-3 Cw ) water concentration in the solvent, mol m-3 dp ) particle diameter, m k ) reaction rate constant, mol1-n s-1 m3n-2 n ) order of reaction r ) reaction rate, mol s-1 rr ) radial position in the reactor, m
2426 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 rs ) reaction rate per unit surface area, mol m-2 s-1 Rr ) radius of the reactor, m ∆Cw ) CSC - Cw, mol m-3 φs ) volume fraction of the solid
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Received for review September 9, 1996 Revised manuscript received February 6, 1997 Accepted February 10, 1997X IE960553B
X Abstract published in Advance ACS Abstracts, April 1, 1997.
